There is an often repeated bit of folklore regarding the path taken by a bullet after leaving the barrel. I've heard people insist that bullets actually rise when they leave the barrel. Others say that it just isn't so. In reality, they are both partially correct.
If you are shooting at something that's at approximately the same height as the sight, the bullet DOES actually rise, but that's because it's being shot uphill!
Since the sight is above the barrel, it's line of sight ( a straight line) starts out above the barrel, and if the centerline of the barrel is absolutely parallel to the line of sight, the bullet's path will never cross the line of sight. As the bullet travels away from the muzzle, gravity pulls it down in an arc, farther and farther below the line of sight, until it finally hits the ground.
To compensate for this, when you sight in, or "zero" your sight, you actually have the barrel aimed slightly uphill, or the sight pointed slightly downhill, depending how you look at it. That results in a spot out in front of the gun where the sight line and the bullet's path cross. That's the left vertical line in the above drawing.
Anything closer, and you have to aim slightly above where you want the bullet to hit. Anything farther away, you have to aim BELOW the intended point of impact to hit the target. As you get farther out, the bullet drops back across the sight line, as at the right vertical line above. At that point you have a second zero, the line of sight and the bullet's point of impact coincide.
When you get even farther to the right, you then have to go back to aiming ABOVE the intended point of impact.
Granted, there are a lot of other factors involved. The closer the center of the sight is to the centerline of the barrel, the less pronounced is this effect. Shooting either uphill or downhill skews the curve of the bullet's path, but the effect is the same. In some cases compensation can be built into the optics, but even so, the the basic principles still apply.
So as you can see, the bullet does often rise coming out of the barrel, but that's just because you are shooting it uphill!